Where is the center of gravity of this system?

In summary: It should.I'm assuming you know what a moment balance is and what the equation for it is.In summary, the center of gravity of this system is located on the line that connects the centers of gravity of the two spheres.
  • #1
timtng
25
0
Two spheres of radius R rest on a horizontal table with their centers a distance 4R apart. One sphere has twice the weight of the other sphere. Where is the center of gravity of this system?

Please help me solve this problem.
 
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  • #2
Well, it's pretty hard to help you if you won't tell us what you do understand about this problem, what you have tried and where you run into a problem.

To start with basics, what do you understand the definition of "center of gravity" to be?
 
  • #3
I think by center of gravity he meant the RADIUS in Fg.

Fg = (G*m1*m2)/R2

R = sqrt((G*m1*m2)/Fg)
 
  • #4
I think by center of gravity he meant the RADIUS in Fg.

Actually, I think you want to approach this like a moment balance problem, where a force of 3Mg (the sum of the weights) is concentrated at the unknown x_cm (center of mass/gravity).
 
  • #5
Prudens Optimus, "You cannot be serious!" Actually, I thought for a very brief moment that he was talking about the gravitational attraction of the two spheres but that doesn't really make sense.

jamesrc: I actually do know what "center of gravity" means! I asked timtng because I wanted to see what HIS understanding of the problem was.


timtng: In other words, shorn of all the unecessary "sphere" stuff, you have a line supporting two weights of mass M and 2M with distance 4R between them and want to find a "fulcrum point" where they will balance. Let x be the distance from mass M to the fulcrum. Mass M has weight Mg and so torque Mgx about the fulcrum. Mass 2M has weight 2Mg. It's distance from the fulcrum is 4R- x so its torque around the fulcrum is 2Mg(4R-x). In order to balance those must be equal: Mgx= 2Mg(4R-x). The first thing you can do is divide the equation by Mg to get x= 2(4R- x)= 8R- 2x. 3x= 8R so x= 8R/3.
 
  • #6
jamesrc: I actually do know what "center of gravity" means! I asked timtng because I wanted to see what HIS understanding of the problem was.

HallsofIvy: I had no doubt of your understanding of the topic; what you were trying to do was quite clear. I just didn't want timtng to remain confused once gravitational attraction was brought into the discussion.
 
  • #7
Ah, I see your point. Thank you.
 
  • #8
why you people questioning timtng question...

he may not be confused...what he means is really center of gravity...
center of gravity not necessarily taken just from one object..

in this case the

assume take point O at the center gravity of smaller sphere.
let w denotes the weight of smaller sphere.

so the Center gravity of the total body =2w*4r / 3w = (8/3)r from point O

it means the center of gravity lies on (5/3)r from lighter sphere or (1/3)r from weighter sphere and this center of gravity should lay in the line which connect the center gravity of lighter sphere and the center gravity from the weight one.

I wish this answer and explanation,will benefits you
 

1. What is the definition of center of gravity?

The center of gravity is the point in a system or object where the weight is evenly distributed and the object is in perfect balance. It is also known as the centroid or center of mass.

2. How is the center of gravity calculated?

The center of gravity can be calculated by finding the weighted average of the individual masses in a system, taking into account their distance from a reference point. This is typically done using mathematical equations and/or computer simulations.

3. Can the center of gravity change?

Yes, the center of gravity can change if the distribution of mass within a system changes. For example, if an object loses or gains mass, or if the position of the masses within the object shifts, the center of gravity will also shift.

4. Why is the center of gravity important?

The center of gravity is important because it affects the stability and balance of a system. If the center of gravity is located outside the base of support, the system will be unstable and prone to tipping over.

5. How does the center of gravity relate to an object's shape?

The location of the center of gravity is dependent on the shape and distribution of mass within an object. Objects with irregular shapes or uneven distribution of mass will have a center of gravity that is more difficult to predict and may be located outside the physical boundaries of the object.

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